# Calculus, triple Integrals, 3D shapes some questions

(say shape of x + y + z) you would not use the r portion i.e. x2 + y2 + z2 = x + y + z, thus the r portion from the circle no use in this part of assessment? - Any unique ways to remember formulas for all shapes(cylinder, cone etc.) - I get confused, f(x,y,z) = formula, great! However with the shapes e.g. z = y + x, the z is not the portion f(x,y,z) etc. The z = x + y shape (its just an example) would just be telling you that "at the z plane you got a drawing of x + y", but to change it into a function it would be f(x,y,z) = -z + x + y?

Im second year part-time self studying student in my later years so be easy. Many thanks!

• Welcome to MSE. I have to confess I find this question completely incoherent. One of the tricky tasks, as a newcomer, is to learn to ask questions well. You need to provide context ("I'm trying to understand how shapes are represented in calculus") and you need to put in enough effort that we're convinced you've done more work than we'll do in providing answers. That includes things like writing in complete sentences, and clearly identifying the question ("So with this in mind, how would I represent the surface of a radius-3 cylinder around the $y$-axis, ranging from $y = -2$ to $y = 2$?"). – John Hughes Apr 12 at 1:14

To be a 3D shape, the equation should only have the variables x, y and z, such as

Sphere with radius r : $$x^2 + y^2 + z^2 = r^2$$

Ellipse with axes a, b and c : $$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$$

Or any shape : f(x, y, z) = a constant

If f(x, y, z) appears in a triple integral, f is only an expression and does not represents a 3D shape such as

$$\iiint_{x^2 + y^2 + z^2 \le r^2} f(x, y, z)dzdydx$$

In this kind of integral the region for the volume has to be specified. The integral just calculates the sum of all the f(x, y, z) values using all the x, y and z value for each point in the region.

I hope you know what I am talking about.

• Thanks that is perfect! – Shaun Weinberg Apr 12 at 19:23